HP 49g manual Polynomials, Horner function

FACTORS:SIMP2:

The functions associated with the ARITHMETIC submenus: INTEGER, POLYNOMIAL, MODULO, and PERMUTATION, are presented in detail in Chapter 5 in the calculator’s user’s guide. The following sections show some applications to polynomials and fractions.

Polynomials

Polynomials are algebraic expressions consisting of one or more terms containing decreasing powers of a given variable. For example, ‘X^3+2*X^2-3*X+2’ is a third-order polynomial in X, while ‘SIN(X)^2-2’ is a second-order polynomial in SIN(X). Functions COLLECT and EXPAND, shown earlier, can be used on polynomials. Other applications of polynomial functions are presented next:

The HORNER function

The function HORNER („Þ, POLYNOMIAL, HORNER) produces the Horner division, or synthetic division, of a polynomial P(X) by the factor (X-a), i.e., HORNER(P(X),a) = {Q(X), a, P(a)}, where P(X) = Q(X)(X-a)+P(a). For example,

HORNER(‘X^3+2*X^2-3*X+1’,2) = {X^2+4*X+5 2 11}

i.e., X3+2X2-3X+1 = (X2+4X+5)(X-2)+11. Also,

HORNER(‘X^6-1’,-5)=

{ X^5-5*X^4+25*X^3-125*X^2+625*X-3125 -5 15624}

i.e., X6-1 = (X5-5*X4+25X3-125X2+625X-3125)(X+5)+15624.

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